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Homeless are created when low-wealth sims do not have any source of income. This does apply only to low wealth sims as medium and high will simply move out and leave the city when they run out of money. Due to the random nature of resources being moved around your city (including the sims) it is possible that you can get homeless even with out an unemployment rate. Certain buildings may just simply not get a return worker to them as they found closer houses to return to of their wealth level.

Homeless will despawn over time but it can take a significant amount of time and they do not help a city in any manner to keep them around. Abandoned buildings will keep them in the city longer. They will also use up slots for visitors to your parks thus reducing their effectiveness.

To actively remove homeless from your town you need to keep your city rid of abandoned buildings and provide a bus system. It is the bus that the homeless will take to leave your town.

It is honestly better however to try and keep ahead of the curve. If you have unemployed within your city you have to remember that building more places for them to work is not the only solution to that situation. You can rezone some of the residential area for a park or the like reducing the population you have while boosting the overall happiness (not land value directly if you use the right parks) of your sims in the area.

I understand now, homeless is the end result of having low-wealth citizens running out of money. I was under the assumption they wouldn't run out of money if I kept 100% citizens working. This is obviously not the case. I am now thinking the only solution may be to change $ workers to $$/$$$ since they seem to be doing fine in my city. It's possible I just have too many $ workers and not enough $$/$$$.
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teeoneMar 20 '13 at 23:14

There was a patch today (1.7) that reports to have improved traffic. This could help in assisting your sims in returning more evenly to houses. I have not had a chance to play with this much yet but will update this if things have changed.
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JamesMar 21 '13 at 6:45